Exact non-Markovian master equation for the spin-boson and Jaynes-Cummings models

Abstract

The spin-boson model describes a qubit coupled to a bosonic bath in thermal equilibrium, and is applicable to a wide range of physical contexts. We show that two weak conditions for the qubit evolution to be Markovian (decreasing system distinguishability and divisibility) are violated at all times t>0, except for a measure-zero set of model parameters. Thus, the recently identified phenomenon of `eternal non-Markovianity' is generic for the spin-boson model. Moreover, there can never be more than one strictly positive decoherence rate, even in the Markovian regime. The main result relies on a recent derivation of the exact form of the master equation. We also show that approximations of the spin-boson model in the literature need not exhibit generic eternal non-Markovianity, indicating the presence of corresponding inherent `Markovian' assumptions.